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• Innovative metamaterial design approach proposed to improve energy absorption capacity. • Varying the structural parameter (D/d) enhanced the metamaterial auxetic effect. • HPH metamaterials absorb energy effectively horizontally with their honeycomb structure. • HPH metamaterials show excellent reusability at lower compression ratios. Hexagonal perforated honeycomb (HPH) metamaterials were designed, fabricated and investigated in this work. Initially, the mechanical properties and deformation modes of various proposed HPH metamaterials (HPH-U, HPH-1 L and HPH-3 L) under quasi-static vertical compression were analyzed using experimental and finite element methods. The findings reveal significant improvements in mechanical properties and energy absorption due to the honeycomb and hierarchical expandable design. Notably, the auxetic effect is diminished. Subsequently, the impact of key dimensional parameters on the mechanical properties and Poisson's ratio behavior was explored. The results highlighted that an increase of elliptical perforation major axis to minor axis ratio enhanced the auxetic effect but compromised load-bearing and absorptive capacity. Additionally, HPH metamaterials displayed exceptional performance under quasi-static horizontal compression, with their honeycomb structure enabling them to withstand both vertical and horizontal impacts while exhibiting excellent energy absorption capabilities. The study also identified relative density as a crucial factor influencing horizontal impact performance. Finally, the study subjected the HPH metamaterials to multiple quasi-static vertical repetitive compressions, meticulously analyzing variations in mechanical properties under diverse compression ratios. Due to distinctive structural design and impressive mechanical properties, HPH metamaterials demonstrate immense potential for applications in automotive engineering and sports protection fields. [Display omitted] [ABSTRACT FROM AUTHOR]

• Classification of the deformation modes of sandwich panels with Miura-ori cores is proposed. • An analytical meso‑scale model of panels' deformation with strong origami cores is developed. • The applicability of the homogenisation approach to the core material properties is analysed. • Experiments were conducted to validate the finite element studies and analytical models. • Comparison of the bending strengths of Miura-ori, PVC and honeycomb core panels is presented. Collapse mechanisms of sandwich panels with Miura-ori cores are analysed and classification of the deformation regimes under three-point bending is proposed. It is revealed that the homogenisation approach to the core material properties is not applicable to the deformation of panels with relatively strong origami cores due to the immediate simultaneous local deformations of the core and face sheets. To describe this deformation regime, an analytical model based on the development of new stationary hinge lines in Miura-ori cells and rigid motion rotation of the adjacent planes is proposed. The model pertains to a single degree-of-freedom model governed by the global bending angle of the panel. On the other hand, the homogenisation approach to the core material properties proved to be applicable to bending analysis of panels with relatively soft Miura-ori cores. This approach is used to analytically obtain the collapse load related to several deformation modes. Parametric FE analysis is conducted to further explore the deformation regimes of panels with different face sheet thicknesses. Experiments were conducted to validate the finite element studies and analytical models. A good agreement between the analytically predicted collapse forces and those obtained by the FE simulations is shown. Deformation mode maps are constructed based on the analytical and FE analyses in terms of the face sheet thicknesses and core strength. A brief comparison between the bending strength of sandwich panels with Miura-ori cores and panels with PVC and honeycomb cores is presented, demonstrating the superiority of the honeycomb cores loaded in the out-of-plane direction. On the other hand, the possibility of the development of high shear strains in metallic Miura-ori cores without damage gives them advantages compared to three-point bending of panels with low density PVC foam cores. [Display omitted] [ABSTRACT FROM AUTHOR]

• The combined effects of bending curvature, loading angle, and thickness on the crushing response of curved honeycombs were clarified in detail. • A macroscopic yield criterion for the initial yield stress of curved honeycombs was presented. • A novel inverse parameter identification method was proposed for the macroscopic yield criterion of curved honeycombs. This paper investigated the initial yield behavior of curved honeycombs under combined shear-compression loads with particular attention to the curvature, loading angle, and honeycomb thickness effects. A detailed finite element model was introduced to analyze the mechanical response and deformation mechanism of curved honeycombs and then verified through experiments using a specially designed set-up. It was found that the curvature had a significant effect on the crushing response. As the curvature increased, the initial peak stress reduced by 16.20%. The out-of-plane loading angle ranging from 0º to 15º had little effect on the crushing behavior, whereas it became more pronounced for the angles larger than 15º. In comparison, the effect of in-plane loading angle fluctuating between 0º and 60º was more significant. Based on the obtained data, a macroscopic yield criterion for the initial yield stress of curved honeycombs was proposed. A novel inverse parameter identification approach for curved honeycombs was proposed to determine the induced parameters conveniently. The current study gave insight into the performance change of honeycombs with specific curvature and could be used to develop its constitutive models under complex loads. [Display omitted] [ABSTRACT FROM AUTHOR]

This paper highlights the effects of cell wall material strain hardening and density functional gradation (FG) on in-plane constant-velocity dynamic crushing response and impact behavior of hexagonal honeycombs. Results show that cell wall material strain hardening influences the distinct deformation modes induced by crushing velocity generally observed in regular hexagonal honeycombs. This is seen by a delay in the onset of localized deformation up until intermediate crushing velocities after which localization becomes dominant smearing out differences brought about by cell wall material strain hardening ( plasticity convergence ). In addition, during the impact loading on regular honeycombs, it was found that increasing the cell wall material strain hardening decreases the rate of gain of maximum crushing strain with increments in initial kinetic energy of impact. On the other hand, introducing FG brings about new deformation patterns due to changes in material distribution and preferential cell wall collapse of the weaker members. Interestingly, although the dynamic localization effect at higher crushing velocities observed earlier was not found to be particularly affected by FG, gradient convergence (i.e. smearing out the effects of FG due to higher velocities analogous to plasticity convergence) was not observed. On the contrary, gradient convergence emerged at higher impacting velocities primarily brought about by a combination of initial deformation localization and its subsequent advancement into FG region ahead. The kinetic energy threshold for the emergence of this gradient convergence effect was found to be considerably delayed by cell wall material strain hardening. [ABSTRACT FROM AUTHOR]

In this paper the dynamics of crush band initiation and wave trapping that result from in-plane impact on a honeycomb are analysed using finite element simulations. The honeycomb structures were loaded in compression at the top surface with a prescribed velocity. Two different boundary conditions were considered; these produced an approximation to a state of uniaxial stress or uniaxial strain at an early state of deformation. The simulations proved that elastic wave propagation had an important effect on crush band initiation, since loading and unloading parts of the compressive wave can reinforce or delay crushing, respectively. Stress enhancement with increasing impact speed is mainly due to translational micro-inertia and not due to micro-rotational inertia. This effect is stronger for uniaxial strain than for uniaxial stress. For the specific case examined here, stress enhancement begins for uniaxial strain at an impact speed of about 1.0 m/s whereas for uniaxial stress it begins at about 10.0 m/s. For the analysed honeycomb the simulation showed for both boundary conditions the existence of a critical impact velocity, so that for impact speeds larger than this critical speed a crush band initiated at the impact surface. For much smaller speeds the location of the initial crush band was determined by the distribution and extent of initial imperfections. In the case of uniaxial stress an analytical estimate of the critical impact speed was derived using the theory of wave trapping. The critical speed depends only on the ratio of the length of the ribbon wall to the length of the thinner inclined wall and the material properties of the constituent material. For the aluminium honeycomb investigated in this paper, wave trapping is predicted to occur for impact speeds greater than 7.6 m/s which is close to the critical speed calculated with the finite element simulations. [Copyright &y& Elsevier]

• A two-stage origami metamaterial with programmable compressive properties is proposed. • The analytical model of the structure is derived for both compressive stages with friction considered. • Numerical simulation and quasi-static crushing tests are carried out and validated with the analytical model. • Influence of the geometric parameters on quasi-static crushing responses of the structure are analysed and compared. An origami metamaterial with two-stage programmable compressive strength is proposed by combining the stacked Miura-origami and rhombic honeycomb structure. By adjusting the geometries of the structure, the compressive response of each stage including the compressive strength and the densification strain can be programmed within a certain range. Furthermore, the initial peak force, as an undesired energy-absorbing characteristic, can be programmed to maintain at a low level. The commonly seen fluctuation of crushing resistance on honeycomb structure is also minimized during the second stage deformation. The crushing behaviour of origami metamaterial is investigated under quasi-static loading condition. The programmability of compressive properties is demonstrated for the two stages of the deformation. The analytical model of the two-stage compressive response of the proposed origami metamaterial is firstly developed with friction contribution being taking into consideration during the first deformation stage. The analytical model is then verified with numerical analysis and quasi-static compressive testing data. The programmability of its compressive properties such as the initial peak crushing resistance, mean crushing force for both stages of deformation are then analysed based on the verified analytical model. Image, graphical abstract [ABSTRACT FROM AUTHOR]